Now class, what's the difference? Anyone? ... Anyone? ... Bueller?
I think you'd better find some different examples Tony. In the case of the shot you included, the nearest-pick looks a little better than the empeg optimized one.

Anyone else from an Amiga background involving a bit of graphics would also know exactly what you're talking about. I'm sure we can find something where the difference is immediately visible. It would probably be better to show the effects on a logo or something with a simpler flat layout (instead of the continuous tone image you started with).
There are more algorithms to do colour reduction and image resampling than you can shake a stick at. It's a shame that none of the big-boy programs like Photoshop and Paint Shop Pro come standard with a larger variety. I used to have a number of excellent image processors on the Amiga that would make short work of this type of conversion.
Bruno